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uly 3l-?3, 1Sl1 The 7th IMT-GT International Conference on Mathematics, Statistics and its Applications 0CMSA 2011)

Table of Contents

Message from NIDA President 8

Message from Dean, the Graduate School of Applied Statistics, NIDA 9

Message from the ICMSA 201 I Chair t0

Conference Sponsors 1I

Organizing Committee t2

Full Paper/ Abstracts I4

Development of Statistical System to Support Effective Decision Making: A Case in Thailand (Abstract Only) Jirawan Baonperm t5

Dynamical Modeling of Delay Mechanisms in Nonlinear Systems in Human Physiology: Delineating Disease and Health (Abstract Only) Yongwimon Lenbury------16

Exponents and Vertex Exponents of Two-colored digraphs (Abstract Only) Saib Suwilo-- 17

Closed-orbit Corurting on Shift Spaces: FromZ to Z" -actions (Abstract OnIy) Mohd Salnri Md Noorani f8

Estisration and Model Selection Basetl on Maximum Product of Spacings for Multivariate Skew Normal Fanrily (Abs tract Only) Arjun K.Gupta 19

Leavitt Path Algebras over Graphs (Abstract Only) Gonzalo Aranda Pino 20

Uniformly Convex Univalent Functions (Absttact OnIy) Rosihan M. .Ali and Y. Ravichandran 2t

Laguerre and Isotropic Surf,aces (Abstract Only)

Y us uf A bu M u hanna. _ _ _ _ _ 22

A Value Function of Discrete Tims Suqplus Process in Insurance under Investment and Reinsurance Credit Risk (Abstract Only) 23 Pairote Sattay atham _ _ _ - - _ _ _ _ _

More Porno, More Sex Crimes? Econometric Analysis of Causal Relationships (Abstract Only) Winai Wonssurawat 24

Out of Crisis Models: An Application of Total Quality Management (TQM) (Abstract Only) Dusit Charern 25

The Statistical Analysis of Self Exciting Point Processes with Applications to Market Research (Abstract Only) Winfried State 26 The 7th IMT-GT International Conference on Mathematics, Statistics and its Applications (rcMSA 2011)

Lyapunov Functionals vs Lyapunov Functions for Various Types of Stability of Hybrid Stochastic Differential Equation (Abstract Only) MahmowdAnabtowi 27

On R.iemann-Liouville and Caputo Impulsive Fractional Calculus M. De laSen 28

On The Pair of Operations With The Generalized Entropic Property AmirEhsani 4*

Applicability of Central Limit Theorem on Machine Generated Random Variables for R.egression Model Aoolinar T. Paulican 46

Hybrid Parameters Methods for The Second Order Initial Value Problems Sesappa A Rai .---.----- 56

History Matching Reservoir Parameter to Different Type of Reservoir Sutawanir Darwis , Agus Yodi Gunawan ,Aceng Komarudin Mutaqin , Nina Fitrivati 66

Modeling Frailty Survival Data Sarhan Haneen, Zubairi Yong Zubairi- 76

Evaluating Advance Efficiency of Bangladeshi Online Banks Using Stochastic Frontier Alalysis Md. Azizul Baten , Anton Abdulbasah Kamil- 85

Love between Two Individuals in a Romantic Relationship: A Newly Proposed Mathematical Model Koushik Ghosh 97

Least Squares Cubic B-spline Finite Elernent Approach to Advection Diffusion Equation S. IA5 S.Dhawan, S. Kumar, Kapaor - - - - -

Heat Transfer and Fluid Flow Characteristic in a Rectangular Cavity with Partial Heating and Cooling at Side Walls Pravez Alam, S.R Ansafi, S. Kapoor.---- tI2

Evaluating Environmenhal Performance in Highway Comtruction Using Neuro-fu24, System and Logistic Regression Analysis

Thoedti.da Thipparat _ _ _ _ t26

Queueing System with Service Channels LinkedUnderPre-emptive Priority Service Rule S. Agrawal, L-M. Tiwari, S-Kapoor, A- Chauhan" R. .R. Siagfr--- t36

Two Levels Regression Modeling of Trading Day and Holiday Effects for Forecasting Retail Data Lee. 150 Suhartono, Muhammad Hisy am - - - - -

Sequential 'Fixed-Ratio Width' Confidence Interval for Reliability Function: Case of Weibull Distribution Rahul Gupta, Yodh Raj, Samit Koul r65

Power of Two-tailed M Test Ros sit aMYrn:u$ S hahj ahan Kh an 172

Statistical Analysis of Various Risk Factors of Tuberculosis (IB) in District Mardan Dr. Salahaddin, Laklekar Khan, Najma 178 The 7th IMT-GT International Conference on Mathematics, Statistics and its Applications (rcMSA 2011)

Estimation in a Random Effects One-way Model: A Multi Stage Approach J P SinghJoorel, Rahul GupIa, S Charak_ 184

Strategizing Planning using MCDM: a Case of Malaysian Local Authorties ldohd Sqhar Sauian, Norbaiatrn Kornaruddia, Ruhaya Atan, I{afsiah Moharued t9I

Motion Planning and Control of a n-LinkNonholonomic Mobile Manipulator Shonal Singh, Bibhya Sharma, Avinesh Prasad 203

Break-^A,nd-Fit Strategy for Bezier and tseta-Splines Curves Normi Abdul ltradi" ,4rsmah lbrokim, Fatimah YahVa, Jamahdin Md Ali. 218

On Upper and Lower tsoundaries of Real Log Canonical Threshold and Free Energy Takeshi Matsuda 226

Parametric Programming and lts Eflects in Determining the Feasible Regron for the Projects in the Developing Counkies Heshow Osnan 236

Outliers Detection in Fuzzy Regression Approach with Asymmetric TrapezoidalFttzzy DaIa A. Maleki 251

Approximate Bayes Estimators of the Pararneters of Weibull Model untler Squared and Enfropy Loss Funcfion Uma Srivastava 258

A dynamically ConsistentNumericalMethod for Sirs Epidemic Model withNon-monotone lncidence Rate 273

Complex Function Bergman Classes with Measures L-F. Res'endis O., L,M. Tovar 5., Ruhan Zhaa 281

Mathematical Modelling of Love Wave in an Anisotropic Porous layer Samit Kumar Vishwalmrma, Shishir Gupta. 297

Nonlinear Extension of Sliced Inverse Regression using the Geodesic Distance Approximation Ilan-Ming l{u 3]2

Trapezoidal FvzyData in Hybrid Fuzzy Regression Analysis T, Razzaghnia 323

Statistical Modeling on Area, Production and Productivity Trends of Mustard (Brassica juncea L. Czern) Crop Rajarathinam A, K Senthamarai Kannan 337

Optimal Sliding Mode Control for Spacecraft Approaching a Tumbling Target Chutiphon Pukdeboan 346

Statistical Inference on Minimax Distribution in the Presence of Outliers Iwan Makhdoom , Pawiz Nasiri- 359

Formation Types of a Flock of I -Trailer Mobile Robots K. Raghuwaiya, S. Srngft, B. Sharma, G. I'ingarn 368 The 7th IMT-GT Tnternational Conference on Mathematics, Statistics and its Applications (rcMSA 2011)

Infant Growth Card by Using Weighted Spline Jerry Dwi Trijoyo Patnoma, I Nyornan Budiontara, Mutiah Sala#Mh, Adi Wicaksono J8J

New Results for Global Asymptotic Stability of Neutral-Type Delayed Neural Networks Ruya Samli. SabriArik 394

A Cyclic Constrained-Search Algorithm for a Two-Stock Universal Portfolio Choon PengTan, Law Heong Pe* 442

Failure Inference of Marker Process Based on Bivariate Gamma Model Soudabeh Shernehssvar 'l I2

Vertex Exponents of 2-digraphs with Largest Exponents Aghni Syahmarani, Saib Suwila ,t24

Fish Processed Froduction Planning Under Uncertainfy Rina Wilyasari, Mardiana lrawafi;, Ilerman Mawengkang 438

Endomorphism Monoid and Group of Cycle Graphs Tinnaluk Rutj anisarakul, Thtuadet Jiarasuksahtn 45$

Marginal Homogeneity Model for Open-ended Categories in Square Contingency Tables Serpil Ahta$. 457

Exponential Extrapolation Method for the Solution of Initial Value Problems in Ordinary Dififerential Equations Asma Elbeleze, Bachok M. Toib 464 '4li

Progressively Type-II Hybrid Censoring Schemes with Log-Normal Distribution Faiba Hemmati, Esmaile Khotraw 174

Vertex and Edge Indepenrlence Sets ofN-gonal Systems Watchara Khuntavic lwL Thiladet Jiarasaksakun- 189

Imaginary Numbers as Quantum Superposition States and a Proof of Complex Vector Conjugation Witald Roman Wiszniew ski 496

Zero-inflatedPoissonVersus Zero-inflatedNegative Binomial: Application to Theft Insurance Data Malina Zulkifii, J,Ioriszura Ismail, Ahnad Mahit Razali- 5tI

Development of Statistical Approximation Model Using Weighted Error Adjustrnent Methods Thipwan Kunihong, Anamai Na-udom, Jaralsi Rwngr*ttanaubol 525

Clayton Copula in Ilandling the Dependence of Claim Severities Yulia Resti, Noriszura Isnail, Saiful Hafuah Ja.amsn 539 lnterval Estimation for Quantile on One Pararneter Exponential Diskibution untler Multiple Type-II Censoring Akhmad Fauzy 547

Towards an Optimal Allocation of the Fiscal Stimulus Package: A Linear Goal Programming Approach Msha El-Ashrawt 55J The ?th IMT-GT International Conference on Mathematics, Statistics and its Applications 0CMSA 201r)

Mode Choice Decision: an Investigation into Suvarnabhumi Airport Rail Link Service Introduction PavitraJindohra 562

Odds Ratio for Contingency Table with Fuzry Categories

Erlo Robert F. Oquendo _ 575

Interval Frediction for Pareto Lifetime Data of Known Shape Parameter under Type-II Censoring with Bayesian Method Epha Diana Sapandi 586

Doubly Multivariate Model Analysis for High Dimensional Multivariate Repeated Measures Kannigar Hiwnkns| Sanruam Chongcharuxn 592

Analysis and Improvement of Non Repeatable Run out Disturbance from Head Stack Assembly in Hard Disk Drive Chaclmphun Aramphongthun, Wanpen Moanl&onburi 6AV

AWell-Defured Interpretation of the Rule of Thumb for the tsernoulli Parameter Sarrprng Ckuang, Wheyming TiaaSong 6t9

Improving Error Control Using Stopping Sets of Codes Chia-Sheng Tsai, You-Kai Xu 626

A F'inite Capacity Scheduling Systern for Assembly Flow Shop with Multiple Cornmon Due Dates: A Case Study

Thanida Khanongnuch, Pisal Yenradee ------632

Aggregate ProductionPlanning withWorkforce Transferring Plan underUncertain Demand and Cost Khiriphach Malmrangkarn, Pisal Yenradee 647

Estimation of A Joined Foint in Tobit-Piecewise Regression Model Titirut Thipbharos 662

Tweaking Naive Bayes Classifier for lntelligent Spam Detection Ankita Rantri, Sunil Pranit La|. 682

Fuzzy Constrained Minimization on Quadratic Programming hoblem Sugiyarto, Yasza Dasril, Ismail Bin Mohd 694

On the Numerical Solution of Linear Stiff IVPs by Modified Homotopy Ferturbation Method M. S. H. Chowdhary,I. Hashim 742

Statistical Analysis on the Reliability Tests in the Resin Coated Transformer Insulation Systems Michael Chuang, Chao-HuagLin, WheymingTinaSong 749

Saw Tooth Function for Enhancing Facial Pattems Detection Using Dynamic Time Warping SornayaAdwan, Hannzak Araf, Haniza Yozid 715

Broadcast Group-oriented Encryption Based on Braid Groups Norranut Saguans akdiyotiq Pipal Hiranvanichakorn 726 The 7th IMT-GT International Conference on Mathematics, Statistics and its Applications (rcMSA 2011)

Clustering of Regencies or Cities in Aceh Province with Principal Component Analysis and Cluster Ana$sis A s ep Ru sy ana, Narhas anah 735

English Mastery Level of FMIPA Unsyiah Graduates Using Binary Logistic Regression Analysis FitrianaA"R 747 hopensity Score Classification in Estimating the Difference between Two Means Marzaki, Nozaruddin 752

FEatwe Selection on Community Health Development Index in Indonesia Using Relief Algorithm Zurnila ]ti{arli Kesumn 758

The Approximation of Bootstrap Residual in Estimating Parameters of Regression Model Msrzuki 766 Nova Ernyda, ------

Study on an EOQ Model with Three-ParameterWeibullDistributionDeterioration without Shortage and Price-Dependent Demand Chandan Kumar Sakrm, Shishir Kums Sahoo 771

Generating Stock Trading Strategies Attawuth Pirom, Ohm Sornit 781 The 7th IMT-GT Tnternational Conference on Mathemafics, Statistics and its Applications (rcMSA 201r) t2

Organizing Committee

International Scientific Committee

Prof. Dr. Herman Mawengkang University of Sumatera Utara, Indonesia Prof. Dato Dr. Rosihan M. Ali Universiti Sains Malaysia,Malaysia Prof. Dr. Yongwimon Lenbury Mahidol University, Thailand Assoc. Prof. Dr. Anton Abdulbasah Kamil Universiti Sains Malaysia,Malaysia Assisf- Prof. Dr. Kanchana Kumnungkit King Mongkuf's Institute of Technology, Ladkrabang, Thail and Assoc. Prof. Dr. Pachitjanut Siripanitch National Institute of Development

Administrati on, Th ail and Assoc- Prof- Dr- Surapong Auwatanamongkol National Institute of Development Administrati on, Thailnnd Assoc. Prof. Adam Baharum Universiti Sains Malaysia, Malaysia Assoc. Prof. Putipong Bookkamana Chiang Mai University, Thailand Dr. Hizir Sofyan Syiah Kuala University, Indonesia Dr. Saib Suwilo University of Sumatera Utzra, Indonesia Dr. Tarmizi Usman Syiah Kuala University, Indonesia Dr. Yosza Dasril Universiti Teknikal Malaysia, Malaysia

Local Organising Committee

Chair: Assoc. Prof. Dr. Surapong Auwatanamongkol

Advisory board:

Prof. Dr. Prachoom Suwattee Assoc. Prof. Dr. Anumongkol Sirivedhin Assoc. Prof. Dr. Vichit Lorchirachoonkul Dr. Lersan Bosuwan The 7th IMT-GT International Conference on Mathematics, Statistics and its Applications (rcMSA2011) 13

Members:

Assoc. Prof. Dr. Duanpen Teerawanviwat Assoc. Prof. Dr. Jirawan Jitthavech Assoc. Prof. Dr- Pachitjanut Siripanitch

Assoc. Prof Dr. Pipat Hiranvanichakorn Assoc. Prof. Dr. Patcharaporn Neammanee

Assoc. Prof. Dr. Raweewan Auepanwiriyakul

Assoc. Prof. Dr. Samruam Chongcharoen Assist. Prof. Dr. lugkain Sukmok Assist. Prof, Dr. Kannapha Amaruchkul Assist. Prof. Dr. Nithinant Thammakounonta Assist. Prof. Dr. Ohm Sornil Assist. Prof. Dr. Pramote Kucharoen Assist. Prof. Dr. Preecha Vichitthamaros

Assist. Prof. Dr. Sukanya Suranauwarat Assist. Prof. Dr. Supoj Sutanthavibul Assist. Prof. Dr. Warapom Jirachiefpattana Assist. hof. Patrawadee Tanawongsuwan Assist. Prof. Weena Chaisilaparungruang Dr. Rattakorn Poonsuph Dr. Siwiga Dusadenoad Dr. Sutep Tongngam Dr. Watchareeporn Chaimongkol lv{r.Worathep Chantakanakakorn The 7th IMT-GT International Conference on Mathematics, Statistics and its Applications (rcMSA20ll) 736

Clustering of Regencies or Cities in Aceh Province with Principal Component Analysis and Cluster Analysis

Asep Rusyanal. Nurhasanah2

r'2Departrnent Mathematics. Faculty of Mathematics and Natural Sciences Unsyiah of tarusyanaGyahoo. com

.Arbstract. Development which is conducted by govemment in Aceh Province has not achieved all arca entitely. It is caused by different condition of each regfficy or city, therefore, policy which is suitable for a regency or city is not sometimes suitable for the others. In the case, govemment of Aceh province needs to look for information about area condition with analyzing indicators which relate to population prcsperity. Objective of the researgh is to iderrti$ chmacteristics ofregencies or cities in Aceh ptovince according to prospercus indicators with principal component analysis (PCA), and cluster analysis. Data is from several surveys which is done by statistic certer board [BPS) in Aceh. The number of variables is 13 which represent population, health, education, housing and income. The first step in the research uses PCA for reduction tolal ofthe variables, so that the number of variables becomes two or three principal components (PC), then cluster analysis is used to cluster PC scores. The reseach results eight clusters of regencies or cities which have similar characteristic among areas in one cluster.

Key words : Pincipal component analysis, clust* analysis, population prospeity

1 INTRODUCTION

l.l Background

Purpose of development in Aceh Province develops population entirely, it does not only provides food, clothes, and housing but also the other need such as : health, education, and work opporfunity. Hence, government must do several strategic programs such as : health, education, housing, and work opportunity. Development is success, if all people in the can get the benefit. Really, development which is done by govemment^rea. has not achieved all regencies or cities. Development of govgmment has not been received entirely in all regencies or cities because condition of the areas which is different, so that policy which is applied for an area, it is not sometimes suitable for the other areas. Therefore, general description of an area is needed so that policy will be suitable. The description can be gotten with analyzing indicators which relate to population prosperity in every regency and city.

ISBN: 978 - 974 - 23r- 812 - 3 The 7th IMT-GT International Conference on Mathematics, Statistics and its Applicafions (rcMsA 2011) 737

In this research, there are 13 variables which can be analtzed and there are correlation among variables. Univariate analysis can not be conducted because it must consider influence of a variable to the others. Facing this problem, multivariate analysis can be held. Multivarate analysis which is used in this research is principal component analysis and cluster analysis.

1.2 Objectives

Purposes ofthe research are: 1 To find principal components which can representative all variables- 2 To cluster regencies or cities according to population prosperous indicators, so it is hoped that there are area clusters which have similar characteristics among areas in the cluster.

2. MATERIALS AND METTIODS

2.lData Source

This research uses secondary data which are resulted from several surveys which are conducted in 23 regencies or cities by Statistic Center Board (BPS). The data, which are 2007,2008, 2009, consist of population data, healthy data, educational data, economical data, and housing data.

2.2Y*iables of The Research

The mrmber of variables is 15 variables which consist of : 1. Percentage of young population ( Xl ) It has age less than 14 years ( 0 - 14 ). The young population is categoried as unproductive people. 2. Percentage of oldpopulation (X2) The population has ages great than 65 years. 3. Population density ( X3 ) The number of person which stays in an area averagely per kilometer sqrEre. 4. Growth of population ( Xa ) Scores which show increase or decrease ofpopulation per year- 5. Percentage of morbidity rate ( X5 ) Person condition which feels disturbed because of health, accident, etc. 6. Average days of illness ( X6 ) 7. Percentage of children under five by birth attendant from doctor or midwife ( X7 ) 8. Percentage of literate adult, which is great than 15 year ( X8 ) The 7th IMT-GT International Conference on Mathematics, Statistics and its Applications (rcMSA 2011) 738

9. Percentage of population who has age great than 10 year and has educational background minimal senior high school ( X9 ) 10. Percentage of poor population ( X10 ) 11. Average of expenditure per person per month ( Xl 1 ) 12. Percentage of households which have floor per person less than 10 meter square ( Xl2 ) 13. Percentage of households which have drinking water from packaging water or running water ( X13 )

2.3 Research Steps

Units of variables are different, so that variables are fransformed to standard variable. Then, the steps are held : 1 Data of variables 2007, 2008, and 2009 are averaged. 2. Data which have been averaged are analyzed using principal component analysis ( PCA ). 3. Determine k first principal components ( PC ) 4. Conduct cluster analysis to data of principal component scores 5. Compare average of each cluster to general average 6. Interpreting of the research results

3. REST]LTS AI\D DISCUSSIONS

Data which are used in the research are data regencies/ cities in 2007, 2008, and 2009 and have units which are different. Therefore, the data are transformed to standard data, then they are averaged. Furthermore, the data are analyzed using PCA. It has resulted eigen value 5.716 for PCl, 2.2Q9 forPC2, and 1.720 for PC3. The other words, proportions of each PC are 0.440, 0.170, and 0.132 so that cumulative proportion is 0-142 which can be called that the three PC can explain variance of the data 74.2 percent ( see Table I ). Plot between PCI and PC2 eanbe seen in Figure 1. It describes location of 23 regencies/ cities in fwo dimension plot. The graph reveals information that Banda Aceh is located on different area from the others. It is caused that the crty has unix character as capital of Aceh province.

ISBN: 978 - 974 - 231- 812 - 3 The 7th IMT-GT International Conference on Mathematics, Statistics and its Applications (rcMSA 2o1l) 739

Table 1. Eigen value, eigen vector, proportion, and cumulative proportion of fhree First Principal Components ( 23 regencies/ cities )

Princioal Comoonent Variable I 2 3 X1 4-2s9 -0.441 0.107 x2 -0.059 0.609 0.068 x3 0.358 -0.043 0.088 x4 -0.10E 0.194 0.3r I x5 -0.187 0.259 0.459 x6 -0.018 0.166 -0.645 x7 0.311 0.080 0-347 x8 0.266 -0.166 0.332 x9 0.405 -0.034 -0.088 x10 -0.317 0.111 0.017 xll 0.358 -0.001 -0.088 xt2 -0.219 -0.497 0.080 x13 0-384 -0.081 0.007 Eieen Value 5.716 2.209 1.720 Proportion o.440 0.170 0.132 Prooortion Cumulative 0.440 0.610 o.742

HdElays O o FI 2 Acshda!€<) G Acehs€* G Abdya Ac€n!ka o hbgeR*.a.} a AceJlBaEt N G a) c Ac€llt-5d-a o 3 ocAcehfageh O kddcefi AcehE @€ Ac€}tsturu Ltr€s -O AcehTffi D<} Lh€g€%ve Sabsg ( Gdrrd-le

PCI Figure 1. Plot of PCI and PC2 scores

ISBN: 978 - 974 - 231- 812 - 3 The 7th IMT-GT International Conference on Mathematics, Statistics and its Applications (rcMSA 2011) 740

Banda Aceh in plot between PCl and PC3 is also located on away area from the other area ( see Figure 2).It is caused because Banda Aceh scores in PC1 is very high. Because of this visual analysis, Banda Aceh will be separated so that position of the other meas can become clearer.

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Figure 2. Plot of PCI and PC3 scores

The next analysis is conducted without Banda Aceh city. PCA is used to 22 regencies or cities, and then three principal components, which can explain 69-7% from data entirely, are resulted ( see Table 2 ) whereas principal component scores of regencies / cities can be seen visually in Figure 3. In the plot, there is not re5ency/ city which lies very far from the others.

ISBN: 978 - 914 - 231- BI2 - 3 The 7th IMT-GT International Conference on Mathematics, Statistics and its Applications (rcMSA 2011) 741

Table 2. Eigen value, eigen vector, proportion, and cumulative proportion of three First Principal Components ( 22 regencies/ cities )

Princinal Component Variable I 2 J XI -0.216 -0.480 0.121 X2 -0.034 0.580 0.080 X3 o.332 -0.065 0.226 x4 -0. I 79 o.242 0.333 x5 -0.105 0.252 0.534 x5 -0.082 0"163 -o.572 x7 0.357 0.068 0.276 x8 0.310 -0.173 o.244 X9 0.428 -0.035 -0.164 xl0 -o.255 0.145 -0.055 xll o323 0.052 -0.157 xl2 -0.235 -0.481 0.1 09 xl3 o.402 -0.087 -0.046 Eieen Value 4.798 2.429 1.837 Pronortion 0.369 i.887 0.143 Proportion Cumulative 0.369 0.556 0 69',1

PCl has positive correlation with X3, X7, )(8, X9, X11, and X13, however it has negative correlation with X10 (see Table 3). It means, PCI has characteristics of population, health, education, economy, and housing. From positive and negative correlation, it can be known that If a regency or city has score of PCl that is high, the area has high population density, children by birth attendant from doctor or midwife, literate adult, population who has senior high school, expenditure, running water or packaging water, yet low poor population. PC2 has positive correlation with X2, but negative correlation with X12. From sign of the correlation, it can be concluded that if an area has high PC2, tho area has high old population, but households which have floor per person less than 10 meter square that is low- PC 3 has positive correlation with X4 and X5, but negative correlation with X6. Therefore, If an area has high PC3 scores, the area has high growth of population and high percentage of morbidity rate, but low average days of illness.

ISBN: 978 - 974 - 231- 812 - 3 The 7th IMT-GT International Conference on Mathematics, Statistics and its Applications 0cMsA20l1) 742

Figure 3. Plot of PCI and PC2 scores

Table 3. Correlation between original variables and three first PC

Variable PCl PC2 PC3 XI -.470 -.748 .168 Yrz -.077 .908 .101 X3 .734 -.1 l0 .322 x4 -.390 .308 .438 X5 -.224 .382 .709 x6 -.180 .256 -.783 x7 .780 .102 .386 X8 .67'.| -.272 .342 x9 .937 -.o5'l -.212 xl0 -,564 .233 -.086 xl1 .703 .079 -.210 xr2 -.5 13 -.746 _150 xl3 .882 -.142 -.053

ISBN: 978 - 974 - 23t- 812 - 3 The 7th IMT-GT International Conference on Mathematics, Statistics and its Applications (rcMSA 2011) 743

Clustering of regency/ city with cluster analysis is shown in dendogram in Figure 4. If the diagram in the figure is cut in 4.5, it will get eight clusters. They are Cluster I Lhoksemawe Cluster 2 Sabang Cluster 3 Gayo Lues Cluster 4 Aceh Singkil, Subulussalam, Simeulu, Aceh Utara, and Aceh Timur Cluster 5 Aceh Jaya, Pidie Jaya, and Pidie Cluster 6 Aceh Selatan, Aceh Barat, Nagan Raya, and Abdya Cluster 7 Aceh Besar Cluster 8 : Aceh Tenggara, LangsE Aceh Tamiang, Aceh Tengah, Bener Meriah, and Bireun If the cluster is compared with plot of PCI and PC2 in Figure 3, visually the result is consistent. Futhermore, each of regencies or cities can be known general description or characteristics with averagrng variable in every cluster ( see Table 4 ). Dendrogram using Average Linkage (Between Groups)

Rescaled Distance Cluster Gorbine 510152025

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Figure 4. Dendogram ofPCl, PC2, PC3 scores

ISBN: 978 - 974 - 23r- 812 - 3 The 7th IMT-GT International Conference on Mathematics, Statistics and its Applications (rcMsA 20rl) 744

Table 4. Averages ofvariables for each cluster

Cluster Variable Average 1 2 J 4 5 6 7 8 XI 30.383" 29.537' 34.627n 35.773h 29.543' 29.592" 28.fi31 31.651" 31.160 X2 2.970" 2.7971 2.6931 3.0w 6394h 4.403' 5.080h 3.567n 3.875 X3 gTlh 191" 13" 72' 129' 48' 104" I 6g' 200 x4 03371 0.097t o.637' 2-295h 4.057h 1.395' o-920" 1.252" r.372 x5 35.600h 16.480r 31.097" 32.223" 36.218n 30.061" 30-457" 31.991" 30.516 X6 4.7201 5.700" 6.920h 5.0911 5.1381 6.901h 5.963" 5.506' 5.742 x7 96333h 96.440h 46.7701 74.762" 83.711r 68.058r 90.167" 87.163" 80.425 x8 98.800h 98.603b 87.587t 95.629" 94.481' 93.865' 95.267" 97.969h 95.275 X9 38.803h 49.637h n.4201 18.9741 21.2]'9r 22.706" 37.813" 3 1.363" 29.742 xl0 14.56?t 25_580" 2't3g0b 26-786" 283ed 26-199' 2Z-'167" 22.O7s" 24.258 xll 4546t1" 628922b 3t7s2d 3366661 371917' 403547" 466983" 389035' 42tt5G xt2 32.130' 29.247u 47 -220h 42J37h 27.2241 29.533" 26.9331 3 1.390' 33.102 xl3 63.360h 81.617h 16.050' 10.1991 15.701' ll326l 32.720" 27.O27" 32.250 Note: l: low; a : averagei h: high

Cluster 1 is Lhoksemawe city. It is known as the second city which is the most advanced after Banda Aceh city. It has high rate on population density ( X3 ), percentage of morbidity rate ( X5 ), children by birth attendant by doctor and midwife ( X7 ), literate adult ( X8 ), population with senior high school background ( X9 ), and households which use running water or package water ( X13 ). Nevertheless, the cluster has tow rate on growth of population ( X4 ), average days of illness ( X6 ), andBercentages of poor population ( XlO ) whereas the other variables show average rate. Cluster 2 is Sabang area. Community knows the area as tourist destination. It has high rate on children by birth attendant by doctor and midwife ( X7 ), literate adult ( X8 ), percentage of population which has senior high school background ( X9 ), expenditure (Xll), households which use running water or package water ( X13 ). However, the cluster has low level on old population ( X2 ), growth of population ( X4 ), and percentage of morbidity rate ( X5 ). Besides that, the area has avarage rate on percentage of young population ( Xl ), population densrty ( X3 ), average days of illness ( X6 ), percentage of poor population ( X10 ) , and percentage of households which have floor per person less than 10 meter square ( X12 ). Cluster 3 is Gayo Lues regency. The regency lies in high land and has cold temperature. Characteristics of the area are high rate on percentage of young population ( Xl ), Lverage days of illness ( X6 ), percentage of poor population ( XlO ), aod percentage of households which have floor per person

ISBN: 978 ^ 974 - 231- 812 - 3 The 7th IMT-GT International Conference on Mathemafics, Statistics and its Applications (rcMSA20r1)

less than l0 meter square (Xlz ). Nevertheless, it has low rate on percentage of old population ( X2 ), percentage of children under five by birth attendant from doctor or midwife (X7 ), percentage of literate adult, which is great than 15 year ( X8 ), and percentage of population who has age great than 10 year and has educational background minimal senior high school ( X9 ). Whereas, the other variables are average level. Cluster 4 consists of four regencies, they are Aceh Singkil, Subulussalam, Simeulu, Aceh Utara, and Aceh Timur. Both Aceh Singkil and Subulussalam lie in westem Aceh, and Simeulu is an island in western Aceh. This cluster has high rate on percentage of young population ( Xl ), growth of population ( X4 ), percentage of households which have floor per person less than 10 meter square (Xlz ). However, it has low rate on average days of illness ( X6 ), percentage of population who has age great than 10 year and has educational background minimal senior high school ( X9 ), average of expenditure per person per month ( Xl1 ), and percentage of households which have drinking water from packaging water or running water ( X13 ). Moreover, the other characteristics seem average. Cluster 5 consists of Aceh Jaya, Pidie Jaya and Pidie. Pidie Jaya was an area of Pidie regency in the past, but It has become a regency since five years ago. The cluster has high rate on percentage of old population ( X2 ), growth of population ( X4 ), percentage of morbidity rate ( X5 ), and percentage of poor population ( Xl0 ). However, the cluster has low rate on average days of illness ( X6 ), percentage of population who has age great than 10 year and has educational background minimal senior high school ( X9 ), and percentage of households which have floor per person less than l0 meter square ( X12 ). Besides that, it has average rate on percentage of young population ( Xl ), population density ( X3 ), percentage of, children under frve by birth attendant from doctor or midwife (X7 ), percentage of literate adult, which is great than 15 year ( X8 ), average of expenditure per person per month ( Xll ), and percentage of households which have drinking water from packaging water or running water ( X13 ). The sixth cluster consists of Aceh Selatan, Aceh Barat, Nagan Raya, and Abdya regency. The regency positions are near each other, therefore, it is not weird if they are located in the same cluster. The cluster has high rate on average days of illness ( X6 ), so that govemement can make a policy for decreasing average days of illness. However, it has low rate on percentage of children under five by birth attendant from doctor or midwife ( X7 ), and percentage of households which have drioking water from packaging water or running water ( X13 ), therefore, goveflrment can increase efforts increasing children which is helped by doctor and midwife, and develop running water in the areas.

ISBN: 978 - 974 - 237- 812 - 3 The 7th IMT-GT International Conference on Mathematics, Statistics and its Applications (rcMSA 201r) 746

The seventh cluster is Aceh Besar Regency. The regency has high rate on percentage of old population ( X2 ), and percentage of literate adult, which is great than 15 year ( X8 ). Nevertheless, it has low rate on percentage of young population ( Xl ). The last cluster consists of 6 areas. They are Aceh Tenggara, Langsa, Aceh Tamiang, Aceh Tengah, Bener Meriah, and Bireun. The cluster has high rate on percentage of literate adult, which is great than l5 year ( X8 )-

4. CONCLUSIONS

1. Banda Aceh, capital of Aceh province, has very diflerent characteristic so it is separated form the analysis. PCl is representave from population density, children by birth attendant from doctor or midwife, literate adult, population who has senior high school, expenditure, running water or packagrng watet, and poor population. PC2 is representative from old population and households which have floor per person less than 10 meter square. And PC 3 is representative from growth of population, percentage of morbidity rate, and average days of illness. J There are eight clusters which have unique characteristics, respectively.

5. ACKNOWLEDGEMENT

The writers thank to department of mathematics. faculty of mathematics Syiah Kuala university which has provided sourcs of the publish funding partly.

PREFERENCES

l Chatfreld, C. & Colin, QA. I.: Introduction to Multivariate Analysis. Chapman and Hall, Newyork. ( 1980 ) 2. Hafu, J. F., er.a/. : Multivariate Data Analysis- Pearson (2010) 3. Johnson, R. A. & Wichem, D. W. : Applied Multivariate Statistical Analysis, Prentice Hall Inc., NewJersey. (1998 ) 4. Morrison : Muhivariate Statistical Methods, McGraw IIi[ Tokyo (1990 ) 5. Ray4 R. Clustering provinces according to population prospcreous level change. ( 2001 )

ISBN: 978 - 974 - 231- 812 - 3